Papers › Inferring the Rotation Period Distribution of Stars from their Projected Rotation...
Inferring the Rotation Period Distribution of Stars from their Projected Rotation Velocities and Radii: Application to late-F/early-G Kepler Stars
Kento Masuda, Erik A. Petigura, Oliver J. Hall
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While stellar rotation periods Pᵣₒₜ may be measured from broadband photometry, the photometric modulation becomes harder to detect for slower rotators, which could bias measurements of the long-period tail of the Pᵣₒₜ distribution. Alternatively, the Pᵣₒₜ distribution of stars can be inferred from their projected rotation velocities vsini and radii R, without being biased against photometrically quiet stars. We solve this inference problem using a hierarchical Bayesian framework, which (i) is applicable to heteroscedastic measurements of vsini and R with non-Gaussian uncertainties and (ii) does not require a simple parametric form for the true Pᵣₒₜ distribution. We test the method on simulated data sets and show that the true Pᵣₒₜ distribution can be recovered from ≳100 sets of vsini and R measured with precisions of 1 km/s and 4%, respectively, unless the true distribution includes sharp discontinuities. We apply the method to a sample of 144 late-F/early-G dwarfs in the Kepler field with vsini measured from Keck/HIRES spectra, and find that the typical rotation periods of these stars are similar to the photometric periods measured from Kepler light curves: we do not find a large population of slow rotators that are missed in the photometric sample, although we find evidence that the photometric sample is biased for young, rapidly-rotating stars. Our results also agree with asteroseismic measurements of Pᵣₒₜ for Kepler stars with similar ages and effective temperatures, and show that ≈1.1 M_⊙ stars beyond the middle of their main-sequence lifetimes rotate faster than predicted by standard magnetic braking laws.
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